A laser vibrometer was used to measure the velocity of a vibrating object at a p

Question

A laser vibrometer was used to measure the velocity of a vibrating object at a particular location. The first six points of the measurement and the initial position are shown in Table 8.1 and illustrated in Figure 8. Initially, the object's position was 0.8 mm. Calculate and fill the values that are missing in Table 8.1. Make the graphs of position and acceleration in Figures N.2 and 8.3. What was the sample rate of the measurement? Write your answer in the box What is the Nyquist frequency for this data record? Write your answer in the box.

Explanation / Answer

a) The sample interval of measurement is 0.05 x 1000 = 50 ms (as it is evident from the graph)

b) Nyquist frequency is half the frequency of the sampling rate, Nyquist = 20 / 2 = 10Hz

c) to fill out the missing values in the table , we will use the following formulae,

i) for calculating the final position we first calculate the distance covered (d) and then add the initial position (Xi) to the distance

X = V*t + Xi

Sample calculation for second step:

X2 = -1.1 x 0.05 + (-1.5 x10-3) = 0.0535 m = 53.5 mm

ii) to calculate the acceleration , we calculate the change in velocity and the time elapsed

i.e., a = V2 - V1 / t2 - t1

Sample calculation:

a2 = (-1.1 - 1.0) / 0.1-0.05 = -42 m/s2

Now , we use excel to fill out the table;

Time (s) Velocity (m/s) Position (mm) Acceleration (m/s2) 0 1 -1.5 0 0.05 -1.1 -56.5 -42 0.1 1.3 73.5 48 0.15 -1.6 -166.5 -58 0.2 1.4 113.5 60 0.25 -0.9 -111.5 -46

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